# Aggregation and Control of Populations of Thermostatically Controlled Loads by Formal Abstractions

arXiv: https://arxiv.org/abs/1307.6716 · HTML: https://mlsanity.com/paper/1307.6716/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2013.

## Built on by (most cited first, 1 of 1)

- [Neural Proofs for Sound Verification and Control of Complex Systems](https://mlsanity.com/paper/2512.18389/) (2025)

## Abstract (arXiv)

This work discusses a two-step procedure, based on formal abstractions, to generate a finite-space stochastic dynamical model as an aggregation of the continuous temperature dynamics of a homogeneous population of Thermostatically Controlled Loads (TCL). The temperature of a single TCL is described by a stochastic difference equation and the TCL status (ON, OFF) by a deterministic switching mechanism. The procedure is formal as it allows the exact quantification of the error introduced by the abstraction -- as such it builds and improves on a known, earlier approximation technique in the literature. Further, the contribution discusses the extension to the case of a heterogeneous population of TCL by means of two approaches resulting in the notion of approximate abstractions. It moreover investigates the problem of global (population-level) regulation and load balancing for the case of TCL that are dependent on a control input. The procedure is tested on a case study and benchmarked against the mentioned alternative approach in the literature.